Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D15×#564 |
| Fitting | C3×C5×#564 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#564 |
| Sylow | C5 ⋊ D3×#564 |
| Sylow | C3 ⋊ D5×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#564 | C2 |
| prime radical | C22×D15 | C24 |
| hypercenter | #564 | D15 |
| hypocenter | C3×C5 | C2×#564 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1792 conjugacy classes of subgroups; only the 601 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 601 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 221278);